Page 88 - Start Up Mathematics_5

4
Example 16: Divide 3 by 15.
7
4
Solution: 3 ÷ 15 = (3 × 7) + 4 ÷ 15 = 21 + 4 ÷ 15
7 7 1 7 1
5

= 25 × 1 = 5 × 1 = 5
7 15 7 × 3 21
3

Division of a fraction by another fraction Remember
To divide a fraction by another fraction:
First fraction ÷ Second fraction
(i) change the sign of division to multiplication. = First fraction × Reciprocal of
second fraction
(ii) multiply the first fraction by the reciprocal of the
second fraction.

3 9
Example 17: Divide by .
8 4
1 1
3 9 3 4 3 × 4 1 × 1 1
Solution: ÷ = × = = =
8 4 8 9 8 × 9 2 × 3 6
2 3
2 14
Example 18: Divide 3 by .
9 27
2 14 (3 × 9) + 2 14 27 + 2 14 29 14
Solution: 3 ÷ = ÷ = ÷ = ÷
9 27 9 27 9 27 9 27
3
= 29 × 27 = 29 × 27 = 29 × 3 = 87 = 6 3
9 14 9 × 14 1 × 14 14 14
1
Properties of division of fractions

2 4 4 2
1. Two fractions cannot be divided in any order. For example, ÷ ≠ ÷ 3
5
5
3
1
4
2 ÷ = × = 2 × 5 = 1 × 5 = 5
5
2
3 5 3 4 3 × 4 3 × 2 6
2
2
4
4 ÷ = × = 4 × 3 = 2 × 3 = 6
2
3
5 3 5 2 5 × 2 5 × 1 5
1
5 6 2 4 4 2
Since ≠ , ÷ ≠ ÷ .
6 5 3 5 5 3
2. When a fraction is divided by itself, the result is 1.
1 1
6 6 6 7 6 × 7 1 × 1
For example, ÷ = × = = = 1
7 7 7 6 7 × 6 1 × 1
1 1

80